Energetic electron bombardment of the H2 atmosphere in the Jovian auroral zone was studied using a theoretical model for the vibrational-ratational excitation processes. A non-relativistic electron energy deposition program originally developed by Peterson et al. was used. Assuming an incident energy electron spectrum from IUE observations, the calculated intensities of the two micron quadrupole lines from the Jovian auroral zone are shown to be comparable to the intensities of infrared objects in the Orion nebula. Jupiter is fairly dark in the 2 to 2.5 micron spectral range because of strong absorption of cH4 and NH3 vibrational-rotational bands. Consequently, assuming no significant decrease in Jovian auroral activity since the Voyager encounter with Jupiter in 1979, the two micron quadrupole emission of H2 may be observable by ground-based telescope through the two micron atmospheric window.